Transport Processes in Liquids of Flexible Chain Molecules/Molecular
Dynamics on the CM-5

The object of these two projects is to provide an understanding of the
microscopic processes underlying transport phenomena in complex liquids. We
develop and use both equilibrium and non-equilibrium molecular dynamics
simulation methods that can be applied to simple or complex liquids. The model
system that we most commonly use for our studies of complex liquids is the
homologous series of n-alkanes. These molecules represent the simplest
examples of non-rigid molecules for which an extensive body of experimental
data exists.

What are the basic questions addressed?

How are macroscopic properties such as the self diffusion coefficient,
viscosity and thermal conductivity related to microscopic processes occurring
in non-equilibrium alkane liquids?

What are the results to date and the future of the work?

The thermal conductivity tensor of shearing liquid butane has been
studied by non-equilibrium molecular dynamics methods. We have found that the
effect of shear on the thermal conductivity tensor is calculable by our
methods, but it is too small to be measured experimentally at the accessible
strain rates. The effect is known to be measurable for polymer melts, but
simulation of such systems will be difficult due to the huge computer power
required.

We have completed a study in which the linear thermal conductivity of liquid
butane has been calculated by non-equilibrium methods using two different
molecular models. The first model was the Ryckaert-Bellemans model, a well
known united atom model, and the second was a more realistic model called the
anisotropic united atom model, which has several improvements over the
Ryckaert-Bellemans model. We found that the new model gives better agreement
with experiment at high temperatures, but it is significantly more difficult to
simulate at low temperatures due to very slow structural relaxations not
present in the Ryckaert-Bellemans model.

Using the CM-5, we have been able to generate very accurate velocity, stress
and heat flux autocorrelation functions for the Ryckaert-Bellemans model of
liquid butane. These correlation functions have allowed us to compute
definitive values for the self diffusion coefficient, viscosity and thermal
conductivity, and have allowed us to critically discuss the scattered values of
these transport coefficients so far published in the literature.

There has recently been some discussion in the literature about the use of
Einstein relations for the computation of collective transport coefficients
such as the viscosity. Although it is known that Einstein relations for
collective transport coefficients, in their standard form, are not compatible
with the periodic boundary conditions usually used in molecular dynamics
simulations, we have found that it is possible to use the non-zero wavevector
forms of these equations for computation.

Future work will include extension of our simulation techniques to simpler
models of chain molecules suitable for studies of long polymers, continuing
studies of coupled transport phenomena in non-equilibrium systems and further
development of our work on Einstein relations in periodic boundary conditions

What computational techniques are used and why is a supercomputer
required?

Our simulation methods employ well vectorized molecular dynamics code
(typically >90% vectorization) on the VP to simulate various models of
alkane liquids. Although the simpler simulations can now be performed on
workstations, our more demanding work on the anisotropic united atom models
requires supercomputers for timely production runs. The computation of
correlation functions on the CM-5 has been greatly expedited by the
introduction of the cloning method, which uses ensemble averaging over
independent initial conditions in addition to time averaging. The superior
speed of convergence of correlation functions calculated in this way has been a
major aid to our understanding of the relations between Einstein and
correlation function expressions for transport coefficients. We intend to make
substantial improvements to our CM-5 code in the near future to enable
simulations of large polymeric systems.